CN107102298B - Radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method - Google Patents

Radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method Download PDF

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CN107102298B
CN107102298B CN201710510046.1A CN201710510046A CN107102298B CN 107102298 B CN107102298 B CN 107102298B CN 201710510046 A CN201710510046 A CN 201710510046A CN 107102298 B CN107102298 B CN 107102298B
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circular array
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CN107102298A (en
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王彤
解彩莲
胡艳艳
李博文
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Xian University of Electronic Science and Technology
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    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a kind of, and the radar covariance matrix based on iteration mutual coupling calibration reconstructs Beamforming Method, its thinking are as follows: determine uniform circular array, the uniform circular array includes M array element, there are Q signal sources in uniform circular array setting range, Q signal source emits Q incoming signal to uniform circular array, and the Q incoming signal includes 1 desired signal and Q-1 interference signal；It obtains the sample covariance matrix R of uniform circular array and carries out feature decomposition, obtain M characteristic value；It calculates the signal MUSIC that incident direction is (θ, φ) to compose, then sets the mutual coupling matrix setup values of uniform circular array, and then obtain the Q azimuth initial value of Q incoming signal, and respectively obtain the final mutual even matrix of uniform circular arrayWith the final bearing of Q incoming signalThen the interference plus noise covariance matrix of uniform circular array after reconstructing is calculatedAnd then the weight vector of the adaptive beam former of uniform circular array is obtained, complete the uniform circular array interference plus noise covariance matrix reconstruct based on iteration mutual coupling calibration.

Description

Radar covariance matrix reconstruction beam forming method based on iterative cross coupling correction
Technical Field
The invention belongs to the technical field of conformal array antenna beam forming, and particularly relates to a radar covariance matrix reconstruction beam forming method based on iterative cross coupling correction, which is suitable for solving the problem that the robustness of a self-adaptive beam former is reduced due to stronger expected signal power in a sampling sample, and the problem that the performance of the beam former is reduced when the cross coupling effect is considered, and improves the robustness of the beam former when the cross coupling effect between array elements is considered.
Background
The conformal array is widely applied due to the advantages of electromagnetic concealment, large scanning angle, small load weight, no interference to the aerodynamic flow field of the flying body and the like; however, conformal array beamforming techniques face several challenges in both theoretical research and development applications. Firstly, the traditional beam forming technology has the defect of insufficient robustness in an actual environment, and the defect still exists when the traditional beam forming technology is applied to a conformal array; in addition, when signals received by the array antenna are transmitted inside the receiving unit, the mutual coupling effect between the array elements cannot be ignored. The complicated array element distribution of the conformal array increases the difficulty of accurately analyzing and modeling the electromagnetic characteristics of the conformal array, so that the mutual coupling correction of the conformal array is very difficult. Therefore, on the premise of fully exerting the advantages of the conformal array, a robust beam forming algorithm is designed, and the problem that the limitation of mutual coupling factors on a beam forming device needs to be solved urgently is broken through.
The theoretical study of adaptive beamforming technology began in the 60's of the 20 th century. Capon proposed a minimum variance distortion free response (MVDR) criterion in 1969 that minimized the output power of the array while ensuring the desired signal gain, providing a theoretical basis for the beamformer to suppress interference. In the 70's of the 20 th century, researchers have proposed a Sampling Matrix Inversion (SMI) algorithm that can adaptively suppress interfering signals using an array received signal snapshot to estimate an interference plus noise covariance matrix. In 1974, Brennan et al derived the probability density function of the output signal-to-interference-and-noise ratio of the SMI beamforming algorithm, and given the relationship between the performance of the adaptive algorithm and the number of training samples.
In many practical application fields, the performance of the adaptive beam former is affected by various error factors, such as signal observation errors, receiving channel errors, array element position errors and the like, and the errors can cause mismatching of steering vectors of received signals of the array antenna, so that the performance of a beam forming algorithm is reduced; moreover, when the sample snapshot contains the desired signal, the mismatching of the steering vectors has a significant effect on the performance of the adaptive beamformer.
In 1991, Benjamin Friedlander and W Anthony J.Weiss propose a DOA estimation method when mutual coupling exists between array elements, which can more accurately estimate the mutual coupling between DOA in the direction of arrival of signals and uniform circular arrays, but the DOA estimation method when mutual coupling exists between array elements is not applied in the technical field of adaptive beam forming; in 2012, Gu proposes a beamforming method based on interference-plus-noise covariance matrix reconstruction, which uses a reconstructed covariance matrix to calculate an adaptive weight vector instead of a covariance matrix of samples contaminated by expectation, and although the method has a good performance when the expected signal power is strong, the method has the following two problems in practical application: first, the method requires that the array configuration be precisely known, the only allowed error is the observation angle error, and the performance is greatly reduced when the mutual coupling effect is considered; second, the method is computationally complex when reconstructing the interference-plus-noise covariance matrix, so that the real-time performance of the algorithm is limited.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention aims to provide a radar covariance matrix reconstruction beam forming method based on iterative cross coupling correction, which performs iterative estimation on an incident angle of a signal and a cross coupling matrix of a uniform circular array, and completes reconstruction of an interference and noise covariance matrix and correction of an expected steering vector by combining an interference and noise covariance matrix reconstruction method, thereby obtaining a more robust beam former under the condition that array elements have cross coupling.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A radar covariance matrix reconstruction beam forming method based on iterative mutual coupling correction comprises the following steps:
step 1, determining a uniform circular array, wherein the uniform circular array comprises M array elements, Q signal sources exist in a set range of the uniform circular array, the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals comprise 1 expected signal and Q-1 interference signals;
acquiring a sampling covariance matrix R of a uniform circular array, and performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array to obtain M characteristic values; m, Q are positive integers greater than 0, Q is greater than 1, M represents the number of array elements included in the uniform circular array, and the value of the number of eigenvalues obtained by performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array is equal to that of the eigenvalues obtained by performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array;
step 2, calculating a signal MUSIC spectrum with an incident direction (theta, phi), then setting a cross coupling matrix initial value of a uniform circular array, and further obtaining Q azimuth angle initial values of Q incident signals, wherein the Q azimuth angle initial values are respectivelyq∈{0,1,2,…,Q-1}，Represents the initial value of the azimuth angle of the q +1 th incident signal;
initialization: let k represent the kth correction, the initial value of k is 1; let the cross-coupling matrix of the uniform circular array after the k-th correction be CkAnd taking Q azimuth angle initial values of the Q incident signals as azimuth angles theta of the Q incident signals after 0-time correction0(ii) a Setting the initial value of the cross-coupling matrix of the uniform circular array as C0，C0＝IM，IMRepresenting an M × M dimensional identity matrix;
step 3, according to the cross coupling matrix C of the uniform circular array after the kth correctionkRespectively estimating the arrival directions of the Q incident signals to obtain the incidence direction (theta) after the kth correctionkPhi) signal MUSIC spectrum PMUSIC(θkPhi), and the azimuth angles of the Q incident signals after the k correction;
step 4, sequentially obtaining the sum J of reciprocal MUSIC spectral values of Q incident signals after the kth correctionckThe cross coupling matrix C of the uniform circular array after the kth correction is obtained through calculation according to the definition formula and the calculation formulak；
Step 5, adding 1 to k, returning to step 3 until Jck-Jc(k-1)<Delta, the correction iteration ends, Jc(k-1)The sum of reciprocal values of MUSIC spectrum values of Q incident signals after the k-1 th correction is represented, delta represents a set threshold value, and a cross coupling matrix C of a corresponding uniform circular array after the k-1 th correction when the correction iteration is stopped is respectively usedkFinal mutual coupling matrix, denoted as uniform circular matrixRecording the azimuth angles of the Q incident signals after the k-th correction corresponding to the stopping of the correction iteration as the final azimuth angles of the Q incident signals
Step 6, according to the final mutual coupling matrix of the uniform circular matrixAnd the final azimuth angle of the Q incident signalsCalculating to obtain an interference and noise covariance matrix of the reconstructed uniform circular array
Step 7, calculating the final steering vector of the expected signal asAnd according to the interference and noise covariance matrix of the reconstructed uniform circular arrayAnd the weight vector of the adaptive beam former of the uniform circular array is calculated to be w, so that the beam forming design of the uniform circular array interference and noise covariance matrix reconstruction based on iterative cross coupling correction is completed.
The invention has the beneficial effects that: firstly, the method for iterative estimation of the mutual coupling matrix of the DOA and the uniform circular array is used for accurately estimating two indispensable parameters in the reconstruction of the interference and noise covariance matrix under the influence of mutual coupling, namely the mutual coupling matrix of the uniform circular array and the azimuth angle of an interference signal, so that the reconstruction of the interference and noise covariance matrix fully carries mutual coupling information, and the robustness of a beam former under the influence of mutual coupling is improved; secondly, the method adopts a method of taking discrete points instead of integration in the interference angle area to reconstruct the interference covariance matrix, thereby reducing the calculation complexity and improving the real-time performance of the algorithm.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a radar covariance matrix reconstruction beam forming method based on iterative mutual coupling correction according to the present invention;
FIG. 2 is a graph of the performance of the method of the present invention as a function of signal-to-noise ratio (SNR) in the presence of observation errors under cross-coupling conditions;
FIG. 3(a) is a graph of the performance of the method of the present invention as a function of sample number for a cross-coupling condition with observation error and an input signal-to-noise ratio of 20 dB;
FIG. 3(b) is a graph of the performance of the method of the present invention as a function of sample number for a cross-coupling condition with observation error and an input signal-to-noise ratio of-5 dB;
FIG. 4 is a graph of the performance of the method of the present invention with SNR change without observation error under cross-coupling conditions;
FIG. 5(a) is a graph of performance of the method of the present invention as a function of sample number without observation error under cross-coupling conditions and with an input signal-to-noise ratio of 20 dB;
FIG. 5(b) is a graph of performance of the method of the present invention as a function of sample number without observation error under cross-coupling conditions and with an input signal-to-noise ratio of-5 dB.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, it is a flowchart of a radar covariance matrix reconstruction beam forming method based on iterative mutual coupling correction according to the present invention; the iterative mutual coupling correction-based radar covariance matrix reconstruction beam forming method comprises the following steps:
step 1, determining a uniform circular array, wherein the uniform circular array comprises M array elements, acquiring a sampling covariance matrix R of the uniform circular array, and performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array to obtain M characteristic values; wherein M is a positive integer greater than 0.
Specifically, a uniform circular array is determined, wherein the uniform circular array comprises M array elements, Q signal sources exist in a set range of the uniform circular array, the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals comprise 1 expected signal and Q-1 interference signals; the distance in the set range is within S kilometers of the uniform circular array, and S is a positive integer greater than 0; in this embodiment, S is 100.
The pitch angle of Q incident signals relative to the uniform circular array is phi, and phi is { phi ═ phi0,φ1,…,φq,…,φQ-1}，q∈{0,1,…,Q-1}，φqRepresents the pitch angle of the q +1 th incident signal with respect to the uniform circular array, and phi0、φ1、…、φq、…、φQ-1The values are respectively equal; phi is a0Representing the pitch angle of the expected signal relative to the uniform circular array, and the pitch angles of the Q-1 interference signals relative to the uniform circular array are phi1、φ2、…、φQ-1。
And acquiring echo data received by the uniform circular array, and performing autocorrelation processing on the echo data received by the uniform circular array to obtain a sampling covariance matrix R of the uniform circular array.
On the premise that the number of expected signals is known to be 1, the number of interference signals is known to be Q-1, and the pitch angle of Q incident signals relative to the uniform circular array is known to be phi, performing characteristic decomposition on a sampling covariance matrix R of the uniform circular array to obtain M characteristic values; because the number of the array elements of the uniform circular array is M, the number of the characteristic values obtained after characteristic decomposition is M.
Sorting M characteristic values obtained after characteristic decomposition from large to small, respectively recording the first Q characteristic values of the M characteristic values sorted from large to small as Q large characteristic values, and recording the rest M-Q characteristic values as M-Q small characteristic values; and taking the eigenvectors corresponding to the first Q large eigenvalues as an expected signal plus interference subspace, recording the eigenvectors corresponding to the M-Q small eigenvalues as a noise subspace, and then performing characteristic decomposition on a uniform circular array sampling covariance matrix R, wherein the decomposition form is as follows:
wherein R is a sampling covariance matrix of a uniform circular array, and the dimension is M multiplied by M; lambdaSIFor diagonal matrices formed by Q large eigenvalues, U, being diagonal elements respectivelySIDesired signal plus interference subspace formed for eigenvectors corresponding to Q large eigenvalues, ΛNFor diagonal matrices formed by M-Q small eigenvalues being diagonal elements, UNA noise subspace is formed by the eigenvectors corresponding to the small eigenvalues of M-Q, the superscript H represents the conjugate transpose operation, M, Q is a positive integer greater than 0, respectively, M is>Q; m represents the number of array elements included by the uniform circular array, and the value of the number of the eigenvalues is equal to the value of the eigenvalues obtained after the sampling covariance matrix R of the uniform circular array is subjected to characteristic decomposition.
Step 2, calculating a signal MUSIC spectrum with the incidence direction (theta, phi), and then setting a cross coupling matrix initial value of a uniform circular array, wherein the signal MUSIC spectrum with the incidence direction (theta, phi) has an initial estimation value; substituting the initial value of the cross coupling matrix of the uniform circular array into the MUSIC spectrum P of the signal with the incidence direction of (theta, phi)MUSICIn the expression (theta, phi), searching the MUSIC spectrum peak in the set azimuth angle range to obtain Q azimuth angle initial values of Q incident signals, wherein the Q azimuth angle initial values are respectively
Specifically, the signal MUSIC spectrum P with the incidence direction (theta, phi)MUSIC(θ, φ), its expression is:
wherein theta represents the azimuth angles of the Q incident signals, phi represents the pitch angles of the Q incident signals relative to the uniform circular array, a (theta, phi) is a signal guide vector with the incident direction being (theta, phi), C is a cross-coupling matrix of the uniform circular array, and the cross-coupling matrix C of the uniform circular array is unknown; u shapeNAnd a superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues.
Setting a mutual coupling matrix initial value C of a uniform circular array0，C0＝IM，IMRepresenting an M × M dimensional identity matrix; the initial value C of the cross coupling matrix of the uniform circular array0Substituted into the signal MUSIC spectrum P with the incident direction of (theta, phi)MUSICIn the expression (theta, phi), searching the MUSIC spectrum peak in the azimuth angle range of 0-180 degrees, and further obtaining Q azimuth angle initial values of Q incident signals, wherein the Q azimuth angle initial values are respectivelyRepresents the initial value of the azimuth angle of the q +1 th incident signal; wherein the range of the set azimuth angle is 0-180 degrees.
Initialization: let k represent the kth correction, the initial value of k is 1; and taking Q azimuth angle initial values of Q incident signals as azimuth angles theta of Q incident signals after 0-time correction0(ii) a Setting the initial value of the cross-coupling matrix of the uniform circular array as C0，C0＝IM，IMRepresenting an M × M dimensional identity matrix.
Step 3, after the characteristic decomposition is finished, under the condition of considering the mutual coupling of the uniform circular arrays, the mutual coupling matrix of the uniform circular arrays after the kth correction is made to be CkAnd according to the cross coupling matrix C of the uniform circular array after the k-th correctionkUsing MUSIC spectrum estimation method to estimate the direction of arrival (DOA) of Q incident signals respectively to obtain the incident direction (theta) after the kth correctionkPhi) signal MUSIC spectrum PMUSIC(θk,φ)。
Specifically, the uniform circular arrays after the k-th correction are consideredCross coupling matrix CkUsing MUSIC spectrum estimation method to estimate the direction of arrival (DOA) of the incident desired signal and Q-1 interference signals, and calculating to obtain the incidence direction (theta) after the kth correctionkPhi) signal MUSIC spectrum PMUSIC(θkPhi), the expression of which is:
wherein, thetakShows the azimuth angle of Q incident signals after the k-th correction, phi shows the pitch angle of the Q incident signals relative to the uniform circular array, a (theta)kPhi) is the incident direction (theta)kPhi) signal steering vector, CkThe cross coupling matrix of the uniform circular array after the kth correction is unknown; u shapeNAnd a superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues.
Since the cross-coupling matrix C of the uniform circular array after the kth correction is unknown, the incident direction is (theta)kPhi) signal MUSIC spectrum PMUSIC(θkPhi) cannot be calculated, the direction of arrival (DOA) of the desired signal and the interfering signal is unknown.
Searching the incidence direction (theta) after the k-th correction in the set azimuth angle rangekPhi) signal MUSIC spectrum PMUSIC(θkPhi) to obtain the azimuth angle theta of Q incident signals after the kth correctionk，θk＝{θ0k,θ1k,…,θqk,…,θ(Q-1)k}，q∈{0,1,…,Q-1}，θqkIndicating the azimuth angle of the q +1 th incident signal after the kth correction; theta0kAzimuth, θ, representing the desired signal after the kth correction1k,θ2k,…,θ(Q-1)kThe azimuth angle of the Q-1 interference signals after the k correction is obtained; wherein the range of the set azimuth angle is 0-180 degrees.
Step 4, defining the sum of reciprocal MUSIC spectrum values of Q incident signals after k correction as JckFrom step 3, after the k-th correctionThe value of the cross coupling matrix of the uniform circular array is equal to that of the actual uniform circular array, and the sum J of the inverses of the MUSIC spectral values of the Q incident signals after the kth correctionckHas a minimum value; if the value of the cross coupling matrix of the uniform circular array after the kth correction is not equal to that of the actual uniform circular array, the sum J of the inverses of the MUSIC spectral values of the Q incident signals after the kth correctionckThere is no minimum value; then let the sum J of the inverse MUSIC values of the k-th corrected Q incident signals in the case that Q azimuth angles of the k-th corrected Q incident signals have been obtainedckThe value is minimum, and then a cross coupling matrix C of the uniform circular array after the kth correction is obtained through calculationk。
The step 4 specifically comprises the following substeps:
(4a) according to the cross coupling matrix C of the uniform circular array after the k-th correctionkDefining the sum of reciprocal MUSIC spectral values of Q incident signals after k correction as JckIt defines the expression:
wherein,indicating a direction of incidence ofSignal steering vector of phiqRepresenting the pitch angle of the q +1 th incident signal with respect to the uniform circular array,indicating the azimuth angle of the q +1 incident signal after the kth correction, | | | | | non-woven cells2The square operation is carried out after the modulus value is taken; ckA cross-coupling matrix, U, being a uniform circular array after the kth correctionNAnd a superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues.
Then, as shown in step 3, the initial estimation value and the real value of the cross-coupling matrix of the set uniform circular matrixIf the cross-coupling matrix values of the adjacent uniform circular arrays are not equal, the sum J of the inverses of the MUSIC spectral values of the Q incident signals after the kth correctionckThere is no minimum value; then, under the condition that Q azimuth angle estimated values of Q incident signals after the k-th correction are obtained, the sum of the reciprocal MUSIC spectral values of the Q incident signals after the k-th correction is made to be minimum, so as to correct the cross-coupling matrix of the uniform circular array, namely, the sum J of the reciprocal MUSIC spectral values of the Q incident signals after the k-th correction is solvedckAnd (5) taking a cross coupling matrix of the uniform circular array after the k-th correction corresponding to the minimum value.
(4b) Since the mutual coupling matrix of a uniform circular array has some special properties: firstly, a cross-coupling matrix of a uniform circular array is a symmetric matrix; secondly, the larger the distance between two adjacent array elements of the uniform circular array is, the smaller the mutual impedance between the two adjacent array elements is; thirdly, the mutual impedance of the array element numbered 2 to the array element numbered 1 is equal to the mutual impedance of the array element numbered 1 to the array element numbered 2 in the geometric structure of the uniform circular array.
Based on the characteristics, the cross coupling matrix C of the uniform circular array after the kth correctionkIs a complex cyclic symmetric matrix, which can be obtained by the cross-coupling matrix C of the uniform circular matrix after the k-th correctionkFirst L in first rowCThe number of the elements is completely determined,represents a round-down operation; and determining a cross-coupling matrix C of the uniform circular matrix after the kth correctionkWith respect to the incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) equivalent to the incident direction being (theta)kPhi) signal steering vector a (theta)kPhi) of M elementsCDimension matrix Q [ a (theta) ]k,φ)]Cross coupling matrix C with k-th corrected uniform circular arraykFirst L of the first rowCComplete composition of LCX 1 dimensional vector ckProduct of (i), i.e. Cka(θk,φ)＝Q[a(θk,φ)]ck。
Wherein, ckA cross-coupling matrix C of the uniform circular array after the k-th correctionkBefore the first row inLCL of one elementCA vector of x 1 dimension is formed,cdkmutual coupling matrix C for expressing uniform circular array after k-th correctionkThe d +1 th element of the first row in (a), the superscript T denoting the transpose operation.
Incident in the direction of (theta)kPhi) signal steering vector a (theta)kPhi) of M elementsCDimension matrix Q [ a (theta) ]k,φ)]By the first MXL after the kth correctionCDimension matrix Q1kThe second MXL after the kth correctionCDimension matrix Q2kThe third MXL after the kth correctionCDimension matrix Q3kAnd the fourth MXL after the kth correctionCDimension matrix Q4kAre added to obtain Q [ a (theta) ]k,φ)]＝Q1k+Q2k+Q3k+Q4kFirst MxL after kth correctionCDimension matrix Q1kThe second MXL after the kth correctionCDimension matrix Q2kThe third MXL after the kth correctionCDimension matrix Q3kAnd the fourth MXL after the kth correctionCDimension matrix Q4kRespectively from the incident direction of (theta)kPhi) signal steering vector a (theta)kPhi), where the first MxL after the kth correctionCDimension matrix Q1kThe elements in the r-th row and the h-th column are Q1(r,h)kSecond MxL after kth correctionCDimension matrix Q2kThe elements in the r 'th row and the h' th column are Q2(r',h')kThe third MXL after the kth correctionCDimension matrix Q3The elements of the r-th row and the h-th column are Q3(r”,h”)kFourth MXL after kth correctionCDimension matrix Q4The middle r 'th row and h' th column elements are Q4(r”',h”')kThe expressions are respectively:
wherein r ∈ {1,2, …, row }1k}，h∈{1,2,…,col1k}，row1kDenotes the first MXL after the kth correctionCDimension matrix Q1kLine number of (col)1kDenotes the first MXL after the kth correctionCDimension matrix Q1kIs given by r' ∈ {1,2, …, row2k}，h'∈{1,2,…,col2k}，row2kIndicates the second MXL after the kth correctionCDimension matrix Q2kLine number of (col)2kIndicates the second MXL after the kth correctionCDimension matrix Q2kColumn number of (r ∈ {1,2, …, row) }3k}，h”∈{1,2,…,col3k}，row3kIndicates the third MXL after the kth correctionCDimension matrix Q3kLine number of (col)3kIndicates the third MXL after the kth correctionCDimension matrix Q3kR' "e {1,2, …, row4k}，h”'∈{1,2,…,col4k}，row4kRepresents the fourth MXL after the kth correctionCDimension matrix Q4kLine number of (col)4kRepresents the fourth MXL after the kth correctionCDimension matrix Q4kThe number of columns of (a) is,represents a rounding up operation; a (theta)k,φ)r+h-1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r + h-1 th element, a (theta)k,φ)r'-h'+1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r '-h' +1 th element, a (theta)k,φ)M+1+r”-h”Indicates an incident direction of (theta)kPhi) signal directorQuantity a (theta)kPhi) element of the M +1+ r '-h' number, a (theta)k,φ)r”'+h”'-M-1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r '″ + h' ″ -M-1 elements; thetakThe azimuth angle of Q incident signals after the k-th correction is shown, and the azimuth angle theta of Q incident signals after the 0-th correction is shown0For Q initial values of the azimuth angle for Q incident signals.
(4c) The mutual coupling matrix property of the uniform circular array described in (4b) can be used to obtain the mutual coupling matrix C of the uniform circular array after the kth correctionkAnd the incident direction ofSignal steering vector ofCan be subject to equivalent substitution, i.e.Wherein, ckA cross-coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCX 1-dimensional vector; further calculating to obtain reciprocal MUSIC spectral values and J of Q incident signals after the kth correctionckThe calculation expression is as follows:
wherein,||||2which means that the square operation is performed after the modulus value is taken.
(4d) For solving the cross-coupling matrix C of the uniform circular matrix after the kth correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckAdding a linear constraint, assuming that the internal self-impedance of array elements of the mutual coupling matrix of the uniform circular array is 1, then Ck(1,1) ═ 1, i.e. eHck1, itThe middle e is an L multiplied by 1 dimensional vector with the first element of 1 and the rest elements of 0, and the following equation is established:
wherein the superscript H denotes the conjugate transpose operation and s.t. denotes the constraint.
Finally, the cross coupling matrix C of the uniform circular array after the kth correction is obtained through calculationkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckThe expression is as follows:
ck＝Gk -1e(eHGk -1e)-1
the cross coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckA cross-coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCCross coupling matrix C of x 1 dimensional vector and uniform circular array after k-th correctionkIs a complex circularly symmetric matrix, so that the cross-coupling matrix C of the uniform circular matrix after the k-th correctionkThe elements in (1) can be obtained by the cross coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckThe middle element is completely determined.
Therefore, according to the cross-coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckCalculating to obtain a cross-coupling matrix C of the uniform circular array after the kth correctionk。
Step 5, adding 1 to k, returning to step 3 until Jck-Jc(k-1)<Delta, the correction iteration ends, Jc(k-1)The sum of reciprocal values of MUSIC spectrum values of Q incident signals after the k-1 correction is represented, delta represents a set threshold value, and the value of delta is 0.0001 in the embodiment; and respectively making the cross-coupling matrix C of the corresponding k-th corrected uniform circular array when the correction iteration is stoppedkIs recorded as uniformFinal mutual coupling matrix of circular matrixThe azimuth angle theta of the Q incident signals after the k correction corresponding to the stopping of the correction iteration is correctedkFinal azimuth, denoted as Q incident signals Representing the final azimuth angle of the q +1 th incident signal after being corrected; then Q final incident directions of Q incident signals are obtained, respectively φqRepresenting the pitch angle of the (q + 1) th incident signal relative to the uniform circular array; wherein,the final direction of incidence of the desired signal.
Step 6, obtaining Q final incidence directions of Q incidence signals and final mutual coupling matrix of uniform circular matrixThen, carrying out interference and noise covariance matrix reconstruction of a uniform circular array; the method comprises the steps of interference covariance matrix reconstruction of a uniform circular array and noise covariance matrix reconstruction of the uniform circular array; and then calculating to obtain an interference and noise covariance matrix of the reconstructed uniform circular array.
The step 6 specifically comprises the following substeps:
(6a) obtaining the final incidence directions of Q-1 interference signals from the final incidence directions of the expected signals removed from the Q final incidence directions of the Q incidence signals
Considering the error of the spectrum estimation algorithm, the azimuth estimation error range is set to be delta theta, so that Q-1 interference signal angle areas can be expressed as
I.e. the final incident directions of the Q-1 interference signals are all locatedInner, and Q-1 interference signal angle regionsThe interference signal detection method comprises Q-1 discrete sampling points, wherein each discrete sampling point corresponds to the final incidence direction of an interference signal; in Q-1 interference signal angle regionRandomly selecting L 'discrete sampling points in the matrix to calculate a covariance matrix, wherein L' is less than or equal to Q-1, and then summing to obtain an interference covariance matrix of the reconstructed uniform circular matrixNamely, it is
Wherein, U represents a union operation, b (θ)l',φl') For Q-1 interference signal angle regionsThe guiding vector at the ith discrete sampling point is 1,2, … and L', and the final mutual matrix of the uniform circular matrix and the Q final incidence directions of the Q incident signals are further usedCalculating to obtain a guide vector b (theta, phi) of the expected signal after mutual coupling correction,therefore, the interference covariance matrix of the reconstructed uniform circular array is obtained by calculationThe expression is as follows:
wherein R represents a sampling covariance matrix of a uniform circular array, b (θ)l',φl') Representing Q-1 interfering signal angular regionsThe guiding vector at the ith discrete sampling point is (theta) with the incident directionl',φl') The values of the signal steering vectors are equal; and then the interference covariance matrix reconstruction of the uniform circular array is completed.
(6b) And reconstructing a noise covariance matrix of the uniform circular array, and performing characteristic decomposition on the sampling covariance matrix of the uniform circular array under an ideal state to obtain M-Q small eigenvalues which are respectively equal, wherein the M-Q small eigenvalues are noise power values.
In practical situations, however, the small M-Q characteristic values are not equal, and for simple calculation, the minimum value of the characteristic values is selected from the small M-Q characteristic values and used as the noise power estimation value of the uniform circular arrayFurther calculating to obtain a noise covariance matrix of the reconstructed uniform circular arrayI denotes an M × M dimensional identity matrix.
(6c) Making uniform circular arrayInterference plus noise covariance matrix reconstruction: interference covariance matrix based on reconstructed uniform circular arrayAnd noise covariance matrix of the reconstructed uniform circular arrayCalculating to obtain an interference and noise covariance matrix of the reconstructed uniform circular arrayThe expression is as follows:
wherein, R represents a sampling covariance matrix of a uniform circular array, and I represents an M multiplied by M dimensional unit matrix; and further, the interference and noise covariance matrix reconstruction of the uniform circular array is completed.
Step 7, calculating the final steering vector of the expected signal asAnd according to the interference and noise covariance matrix of the reconstructed uniform circular arrayAnd calculating to obtain a weight vector w of the adaptive beam former of the uniform circular array by utilizing a Linear Constraint Minimum Variance (LCMV) criterion, and further completing the beam forming design of the reconstruction of the uniform circular array interference and noise covariance matrix based on iterative cross coupling correction.
Specifically, the final steering vector of the desired signal is calculated as Is incident in the direction ofThe signal of (a) is directed to a vector,and calculating a weight vector w of the adaptive beam former of the uniform circular array by using a Linear Constrained Minimum Variance (LCMV) rule for the final incidence direction of the expected signal, wherein the expression is as follows:
wherein, the superscript-1 represents the inversion operation, and the superscript H represents the conjugate transpose operation; and further completing the beam forming design of the uniform circular array interference and noise covariance matrix reconstruction based on the iterative cross coupling correction.
The effect of the present invention is further verified and explained by the following simulation experiment.
Simulation conditions
The simulation experiment of the invention is carried out under MATLAB software, in the experiment of the invention, a uniform circular array adopts 10 array elements, the signal wavelength of Q incident signals is set to be 0.1 meter, the ratio d/lambda of the distance d between adjacent array elements and the signal wavelength of Q incident signals is 0.5, the pitch angle of each incident signal relative to the uniform circular array is set to be 30 degrees, the azimuth angle of an expected signal is set to be 95 degrees, two interference signals are set, and the azimuth angles of the two interference signals are respectively 50 degrees and 140 degrees.
The specific algorithm parameters are shown in the following table:
(II) simulation content and result analysis
To illustrate the superiority of the algorithm of the present invention, fig. 2 to 5 show the processing results of several other beamforming algorithms, including an optimal beamformer, a Sampling Matrix Inversion (SMI) beamformer, a covariance matrix reconstruction algorithm and a worst-case performance optimization method.
The horizontal axis of fig. 2 represents the input signal-to-noise ratio and the vertical axis represents the output signal-to-interference-and-noise ratio; fig. 2 shows a graph of the variation of the output sir of several beamforming methods with the input sir of the desired signal in the presence of signal observation errors and a fast sampling rate of 30. As can be seen from fig. 2, in the presence of both cross coupling effect and incident signal observation error, the performance of the common covariance matrix reconstruction method is drastically reduced, and the performance is even far inferior to that of the SMI method in a low signal-to-noise ratio scene; the worst-performance optimized beam forming method has better performance robustness, but the gap between the performance of the worst-performance optimized beam forming method and a theoretical optimal value is increased when the expected signal power is stronger; the performance of the covariance matrix reconstruction method based on mutual coupling correction provided by the invention is extremely close to a theoretical optimal value under the condition of high signal-to-noise ratio, and the performance of the algorithm is reduced under the condition of low signal-to-noise ratio, because the DOA estimation is misaligned when the expected signal power is lower than the noise level, thereby affecting the performance of the beam former.
The horizontal axis of fig. 3(a) and 3(b) represents the number of sample samples, and the vertical axis represents the output signal-to-interference-and-noise ratio of the beamformer; FIG. 3(a) shows the simulation results in the presence of a signal observation error with an input signal-to-noise ratio of 20dB, and FIG. 3(b) shows the simulation results in the presence of a signal observation error with an input signal-to-noise ratio of-5 dB. Simulation results show that when the input signal-to-noise ratio of the expected signal is higher, the beam forming method provided by the invention has greatly superior performance to other beam forming methods; the beamforming algorithm provided by the invention still has good performance if sufficient samples can be ensured under the condition of low signal-to-noise ratio.
The horizontal axis of fig. 4 represents the input signal-to-noise ratio and the vertical axis represents the output signal-to-interference-and-noise ratio; fig. 4 shows a plot of the output sir for several beamforming methods as a function of the input sir of the desired signal without signal observation error and with a fast sampling rate of 30. As can be seen from fig. 4, under the condition that only the mismatching of the steering vectors of the desired signal and the interference signal caused by the mutual coupling of the uniform circular array is considered, after the mutual coupling correction of the method, the performance of the beam former is almost not different from the theoretical optimal value under the condition of high signal-to-noise ratio, because the method only corrects the mutual coupling factor, removes the desired signal component in the sampling covariance matrix, and can achieve the performance close to the theoretical optimal value without considering other mismatching factors.
The horizontal axis of fig. 5(a) and 5(b) represents the number of sample samples, and the vertical axis represents the output signal-to-interference-and-noise ratio of the beamformer; FIG. 5(a) shows the simulation results when there is no signal observation error and the input signal-to-noise ratio is 20dB, and FIG. 3(b) shows the simulation results when there is no signal observation error and the input signal-to-noise ratio is-5 dB. The result shows that the performance of the method is better than that of the method considering signal observation errors under the condition that the guide vectors of the expected signal and the interference signal are mismatched due to the mutual coupling of the uniform circular arrays.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the method.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (4)

1. A radar covariance matrix reconstruction beam forming method based on iterative mutual coupling correction is characterized by comprising the following steps:
step 1, determining a uniform circular array, wherein the uniform circular array comprises M array elements, Q signal sources exist in a set range of the uniform circular array, the Q signal sources transmit Q incident signals to the uniform circular array, and the Q incident signals comprise 1 expected signal and Q-1 interference signals;
acquiring a sampling covariance matrix R of a uniform circular array, and performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array to obtain M characteristic values; m, Q are positive integers greater than 0, Q is greater than 1, M represents the number of array elements included in the uniform circular array, and the value of the number of eigenvalues obtained by performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array is equal to that of the eigenvalues obtained by performing characteristic decomposition on the sampling covariance matrix R of the uniform circular array;
in the step 2, the step of mixing the raw materials,calculating MUSIC spectrum of signal with incidence direction (theta, phi), setting initial value of cross coupling matrix of uniform circular array, and obtaining Q initial values of azimuth angles of Q incident signalsq∈{0,1,2,…,Q-1}，Represents the initial value of the azimuth angle of the q +1 th incident signal;
initialization: let k represent the kth correction, the initial value of k is 1; let the cross-coupling matrix of the uniform circular array after the k-th correction be CkAnd taking Q azimuth angle initial values of the Q incident signals as azimuth angles theta of the Q incident signals after 0-time correction0(ii) a Setting the initial value of the cross-coupling matrix of the uniform circular array as C0，C0＝IM，IMRepresenting an M × M dimensional identity matrix;
step 3, according to the cross coupling matrix C of the uniform circular array after the kth correctionkRespectively estimating the arrival directions of the Q incident signals to obtain the incidence direction (theta) after the kth correctionkPhi) signal MUSIC spectrum PMUSIC(θkPhi), and the azimuth angles of the Q incident signals after the k correction;
step 4, sequentially obtaining the sum J of reciprocal MUSIC spectral values of Q incident signals after the kth correctionckThe cross coupling matrix C of the uniform circular array after the kth correction is obtained through calculation according to the definition formula and the calculation formulak；
Step 5, adding 1 to k, returning to step 3 until Jck-Jc(k-1)< Δ, the correction iteration ends, Jc(k-1)Expressing the sum of reciprocal MUSIC spectral values of Q incident signals after the k-1 th correction, and expressing the set threshold value by delta, and respectively stopping the correction iteration by the cross coupling matrix C of the corresponding uniform circular array after the k-th correctionkFinal mutual coupling matrix, denoted as uniform circular matrixWhen the correction iteration is stoppedThe azimuth angles of the Q incident signals after the corresponding k-th correction are recorded as the final azimuth angles of the Q incident signals
Step 6, according to the final mutual coupling matrix of the uniform circular matrixAnd the final azimuth angle of the Q incident signalsCalculating to obtain an interference and noise covariance matrix of the reconstructed uniform circular array
And 7, calculating to obtain a final guide vector of the expected signal, and according to the interference and noise covariance matrix of the reconstructed uniform circular arrayThe weight vector of the adaptive beam former of the uniform circular array is calculated to be w, and then the beam forming design of the uniform circular array interference and noise covariance matrix reconstruction based on iterative cross coupling correction is completed;
wherein, in step 1, the Q incident signals further include:
the pitch angle of Q incident signals relative to the uniform circular array is phi, and phi is { phi ═ phi0,φ1,…,φq,…,φQ-1}，q∈{0,1,…,Q-1}，φqRepresents the pitch angle of the q +1 th incident signal with respect to the uniform circular array, and phi0、φ1、…、φq、…、φQ-1The values are respectively equal; phi is a0Representing the pitch angle of the expected signal relative to the uniform circular array, and the pitch angles of the Q-1 interference signals relative to the uniform circular array are phi1、φ2、…、φQ-1；
And carrying out characteristic decomposition on the sampling covariance matrix R of the uniform circular array, wherein the decomposition form is as follows:
wherein R is a sampling covariance matrix of a uniform circular array, and the dimension is M multiplied by M; lambdaSIFor diagonal matrices formed by Q large eigenvalues, U, being diagonal elements respectivelySIDesired signal plus interference subspace formed for eigenvectors corresponding to Q large eigenvalues, ΛNFor diagonal matrices formed by M-Q small eigenvalues being diagonal elements, UNA superscript H represents a conjugate transposition operation for a noise subspace formed by eigenvectors corresponding to the small eigenvalues of M-Q, M, Q are positive integers greater than 0 respectively, and M is greater than Q; m represents the number of array elements included by the uniform circular array, and the number of array elements is equal to the value of the eigenvalue obtained after the sampling covariance matrix R of the uniform circular array is subjected to characteristic decomposition;
in step 2, the signal MUSIC spectrum P with the incidence direction of (theta, phi)MUSIC(θ, φ), its expression is:
wherein theta represents the azimuth angle of Q incident signals, phi represents the pitch angle of the Q incident signals relative to the uniform circular array, a (theta, phi) is a signal guide vector with the incident direction (theta, phi), C is a cross-coupling matrix of the uniform circular array, U is the cross-coupling matrix of the uniform circular array, andNa superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues;
the process of obtaining Q azimuth initial values of Q incident signals is as follows:
setting a mutual coupling matrix initial value C of a uniform circular array0，C0＝IM，IMRepresenting an M × M dimensional identity matrix; the initial value C of the cross coupling matrix of the uniform circular array0Substituted into the signal MUSIC spectrum P with the incident direction of (theta, phi)MUSICIn the expression (theta, phi), searching MUSIC spectrum peak in the azimuth angle range of 0-180 DEG, and further obtaining QQ initial values of azimuth angle of incident signal areq∈{0,1,2,…,Q-1}，Represents the initial value of the azimuth angle of the q +1 th incident signal; wherein the range of the set azimuth angle is 0-180 degrees;
in step 3, the incidence direction after the k time correction is (theta)kPhi) signal MUSIC spectrum PMUSIC(θkPhi), the expression of which is:
wherein, thetakShows the azimuth angle of Q incident signals after the k-th correction, phi shows the pitch angle of the Q incident signals relative to the uniform circular array, a (theta)kPhi) is the incident direction (theta)kPhi) signal steering vector, CkA cross-coupling matrix, U, being a uniform circular array after the kth correctionNA superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues;
searching the incidence direction (theta) after the k-th correction in the set azimuth angle rangekPhi) signal MUSIC spectrum PMUSIC(θkPhi) to obtain the azimuth angle theta of Q incident signals after the kth correctionk，θk＝{θ0k,θ1k,…,θqk,…,θ(Q-1)k}，q∈{0,1,…,Q-1}，θqkIndicating the azimuth angle of the q +1 th incident signal after the kth correction; theta0kAzimuth, θ, representing the desired signal after the kth correction1k,θ2k,…,θ(Q-1)kThe azimuth angle of the Q-1 interference signals after the k correction is obtained; wherein the range of the set azimuth angle is 0-180 degrees;
the substep of step 4 is:
(4a) according to the k-th correctionCross coupling matrix C of rear uniform circular arraykDefining the sum of reciprocal MUSIC spectral values of Q incident signals after k correction as JckIt defines the expression:
wherein,indicating a direction of incidence ofSignal steering vector of phiqRepresenting the pitch angle of the q +1 th incident signal with respect to the uniform circular array, indicating the azimuth angle of the q +1 incident signal after the kth correction, | | | | | non-woven cells2The square operation is carried out after the modulus value is taken; ckA cross-coupling matrix, U, being a uniform circular array after the kth correctionNA superscript H represents a conjugate transpose operation for a noise subspace formed by eigenvectors corresponding to the M-Q small eigenvalues;
(4b) determining a cross-coupling matrix C of the uniform circular array after the kth correctionkCross coupling matrix C of uniform circular array after k-th correctionkFirst L in first rowCThe number of the elements is completely determined, represents a round-down operation; and determining a cross-coupling matrix C of the uniform circular matrix after the kth correctionkWith respect to the incident direction of (theta)kPhi) signal steering vector a (theta)kMultiplication of phi)Product, equivalent to the incident direction being (θ)kPhi) signal steering vector a (theta)kPhi) of M elementsCDimension matrix Q [ a (theta) ]k,φ)]Cross coupling matrix C with k-th corrected uniform circular arraykFirst L of the first rowCComplete composition of LCX 1 dimensional vector ckProduct of (i), i.e. Cka(θk,φ)＝Q[a(θk,φ)]ck；
Wherein, ckA cross-coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first rowCL of one elementCA vector of x 1 dimension is formed,d∈{0,1,…,LC-1}，cdkmutual coupling matrix C for expressing uniform circular array after k-th correctionkThe (d + 1) th element in the first row, the superscript T representing the transpose operation;
incident in the direction of (theta)kPhi) signal steering vector a (theta)kPhi) of M elementsCDimension matrix Q [ a (theta) ]k,φ)]By the first MXL after the kth correctionCDimension matrix Q1kThe second MXL after the kth correctionCDimension matrix Q2kThe third MXL after the kth correctionCDimension matrix Q3kAnd the fourth MXL after the kth correctionCDimension matrix Q4kAre added to obtain Q [ a (theta) ]k,φ)]＝Q1k+Q2k+Q3k+Q4kFirst MxL after kth correctionCDimension matrix Q1kThe second MXL after the kth correctionCDimension matrix Q2kThe third MXL after the kth correctionCDimension matrix Q3kAnd the fourth MXL after the kth correctionCDimension matrix Q4kRespectively from the incident direction of (theta)kPhi) signal steering vector a (theta)kPhi), where the first MxL after the kth correctionCDimension matrix Q1kThe elements in the r-th row and the h-th column are Q1(r,h)kSecond MxL after kth correctionCDimension matrix Q2kThe elements in the r 'th row and the h' th column areQ2(r',h')kThe third MXL after the kth correctionCDimension matrix Q3The elements of the r-th row and the h-th column are Q3(r”,h”)kFourth MXL after kth correctionCDimension matrix Q4The middle r 'th row and h' th column elements are Q4(r”',h”')kThe expressions are respectively:
wherein r ∈ {1,2, …, row }1k}，h∈{1,2,…,col1k}，row1kDenotes the first MXL after the kth correctionCDimension matrix Q1kLine number of (col)1kDenotes the first MXL after the kth correctionCDimension matrix Q1kIs given by r' ∈ {1,2, …, row2k}，h'∈{1,2,…,col2k}，row2kIndicates the second MXL after the kth correctionCDimension matrix Q2kLine number of (col)2kIndicates the second MXL after the kth correctionCDimension matrix Q2kColumn number of (r ∈ {1,2, …, row) }3k}，h”∈{1,2,…,col3k}，row3kIndicates the third MXL after the kth correctionCDimension matrix Q3kLine number of (col)3kIndicates the third MXL after the kth correctionCDimension matrix Q3kR' "e {1,2, …, row4k}，h”'∈{1,2,…,col4k}，row4kRepresents the fourth MXL after the kth correctionCDimension matrix Q4kLine number of (col)4kIs shown asFourth MxL after k times of correctionCDimension matrix Q4kThe number of columns of (a) is, represents a rounding up operation; a (theta)k,φ)r+h-1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r + h-1 th element, a (theta)k,φ)r'-h'+1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r '-h' +1 th element, a (theta)k,φ)M+1+r”-h”Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) element of the M +1+ r '-h' number, a (theta)k,φ)r”'+h”'-M-1Indicates an incident direction of (theta)kPhi) signal steering vector a (theta)kPhi) the r '″ + h' ″ -M-1 elements; thetakThe azimuth angle of Q incident signals after the k-th correction is shown, and the azimuth angle theta of Q incident signals after the 0-th correction is shown0Q azimuth initial values for Q incident signals;
(4c) determining a cross-coupling matrix C of the k-th corrected uniform circular arraykAnd the incident direction ofSignal steering vector ofBy making equivalent substitution, i.e.Wherein, ckA cross-coupling matrix C of the uniform circular array after the k-th correctionkFirst L of the first row ofCL of one elementCX 1-dimensional vector; further calculating to obtain reciprocal MUSIC spectral values and J of Q incident signals after the kth correctionckThe calculation expression is as follows:
wherein,|| ||2the square operation is carried out after the modulus value is taken;
(4d) the following equation is established:
wherein e is an L multiplied by 1-dimensional vector with a first element of 1 and the rest elements of 0, the superscript H represents the conjugate transpose operation, and s.t. represents the constraint condition;
then calculating to obtain a cross coupling matrix C of the uniform circular array after the kth correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckThe expression is as follows:
ck＝Gk -1e(eHGk -1e)-1
finally, according to the cross coupling matrix C of the uniform circular array after the kth correctionkFirst L of the first row ofCL of one elementCX 1 dimensional vector ckCalculating to obtain a cross-coupling matrix C of the uniform circular array after the kth correctionk。
2. The iterative mutual coupling correction-based radar covariance matrix reconstruction beamforming method of claim 1 wherein in step 5, the final azimuth angles of the Q incident signalsThe method specifically comprises the following steps:
final azimuth angle of Q incident signals Representing the final azimuth angle of the q +1 th incident signal after being corrected; then Q final incident directions of Q incident signals are obtained, respectivelyφqRepresenting the pitch angle of the (q + 1) th incident signal relative to the uniform circular array; wherein,the final direction of incidence of the desired signal.
3. The iterative mutual coupling correction-based radar covariance matrix reconstruction beamforming method of claim 2 wherein in step 6, the interference-plus-noise covariance matrix of the reconstructed uniform circular arrayThe obtaining process comprises the following steps:
(6a) obtaining the final incidence directions of Q-1 interference signals from the final incidence directions of the expected signals removed from the Q final incidence directions of the Q incidence signals
Setting the error range of azimuth angle estimation as delta theta, and representing the Q-1 interference signal angle areas as
The final incidence directions of the Q-1 interference signals are all positionedInner, and Q-1 interference signal angle regionsThe interference signal detection method comprises Q-1 discrete sampling points, wherein each discrete sampling point corresponds to the final incidence direction of an interference signal; in Q-1 interference signal angle regionRandomly selecting L 'discrete sampling points in the matrix to calculate a covariance matrix, wherein L' is less than or equal to Q-1, and then summing to obtain an interference covariance matrix of the reconstructed uniform circular matrixThe expression is as follows:
wherein, U represents a union operation, b (θ)l',φl') For Q-1 interference signal angle regionsThe guiding vector at the ith discrete sampling point is (theta) with the incident directionl',φl') The values of the signal steering vectors are equal; 1,2, …, L';
(6b) calculating to obtain a noise covariance matrix of the reconstructed uniform circular arrayI represents an M × M dimensional identity matrix; wherein,indicates uniformityA noise power estimate of the circular array;
(6c) interference covariance matrix based on reconstructed uniform circular arrayAnd noise covariance matrix of the reconstructed uniform circular arrayCalculating to obtain an interference and noise covariance matrix of the reconstructed uniform circular arrayThe expression is as follows:
wherein, R represents a sampling covariance matrix of a uniform circular array, and I represents an M multiplied by M dimensional identity matrix.
4. The iterative mutual coupling correction-based radar covariance matrix reconstruction beamforming method of claim 3 wherein in step 7, the final steering vector of the desired signal is Is incident in the direction ofThe signal of (a) is directed to a vector,for final input of desired signalsA shooting direction;
the weight vector w of the adaptive beam former of the uniform circular array has the expression:
where the superscript-1 denotes the inversion operation and the superscript H denotes the conjugate transpose operation.
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